Flat Jet Research Articles

PRINCIPLES OF SIMULATION OF ENERGY-EFFICIENT GRANULATION PROCESSES IN A FLUIDIZED BED

The principles of physical and mathematical modeling of inhomogeneous jet-pulsating fluidization in the self-oscillating mode considering the movement of solid granulated particles on the working surfaces of the gas distributing device are investigated. The research tasks include substantiating the method of interaction between the gas phase and granular solids to ensure the implementation of heterogeneous jet-pulsating fluidization in the self-oscillating mode, experimentally determining hydrodynamic parameters to minimize the risk of stagnant zones on the working surface of the gas distributing device and formulating principles for introducing flat gas jets into orthogonal planes through a gas distribution device. The physical model focuses on creating heterogeneous jet-pulsating fluidization which is based on the formation of heterogeneous porosity in the bed of solids within the apparatus chamber. The study highlights the importance of rationally organizing the interaction mode between the gas phase and solids to ensure active circulation of granular material between 3 main technological zones: humidification, active heat exchange and relaxation. This organization enables sufficient mass transfer along the height of the bed and getting a product with the desired properties. Implementing the proposed modeling principles in equipment development will allow increasing the heat utilization coefficient by more than 60 % and will facilitate the implementation of innovative technology. The research contributes to the development of fluidization technology and its application in granulation at temperatures exceeding the melting point of thermolabile components, ensuring efficient use of resources and energy, and enhancing the environmental safety of technological processes. Bibl. 22, Fig. 11.

Liquid crystal-based temperature-controlled recirculating flat jet system.

In this paper, the design and implementation of a temperature-controlled recirculating flat jet system for liquid crystals (LCs)-based experiments are presented. In these experiments, the target liquid is usually exposed to medium to high laser fluences, possibly resonant with specific excitation, thus resulting in a change of local temperature and sudden degradation. To overcome this problem, each laser pulse must interact with a new volume of liquid, preferably with flat surfaces, while avoiding the use of substrates. A well-established solution consists of impinging two identical laminar jets that force the liquid into a radial expansion perpendicular to the plane formed by the jets, resulting in a consecutive chain of flat sheets bound by thick rims. In this context, LCs pose several challenges considering their viscosity, non-Newtonian behavior, and mesophase nature. Here, a precise control of temperature, thus mesophase, and pressure is demonstrated enabling the use of LCs in an impinging jet system. In particular, the system presented here delivers stable fluid chains of different sizes and thicknesses. The viscosity and non-Newtonian behavior of the LCs have a significant impact on the thickness of the chains as a function of the nozzle inner diameter, impinging angle, and radial distance from the impinging point. The flow rate, on the other hand, primarily affects the width and length of the liquid sheet.

Influence of corrugated jet plates on internal heat transfer and flow dynamics of double-wall cooling: experimental-numerical approach

In the present study, combined experimental and numerical investigations were carried out to analyze the fluid flow dynamics and heat transfer of impinging jets in a corrugated double-wall structure for exhaust nozzle cooling operating at high temperatures. The sinusoidal wavy plate, with multi-jet holes positioned at its trough, served as the jet plate, creating a staggered configuration with respect to the effusion holes. The transient thermochromic liquid crystal (TLC) method was employed to determine the local distribution of the Nusslet number on the flat effusion plate in a wind tunnel at small Reynolds numbers (ranging from 450 to 2700 based on the jet hole diameter (d)). In the numerical part of the study, the k-ω SST turbulence model verified with the TLC data was used to solve the RANS equations. The effects of jet-to-plate spacing (Have/d = 1.6–3.6), corrugated plate amplitude (A/d = 0.2–0.8), effusion hole diameter (de/d = 0.6–1.5), and Reynolds numbers were examined in detail. Our results showed that the introduction of the corrugated structure in the jet plate altered the high-velocity region pattern within the jet hole, leading to a 16 %-81 % reduction in jet core length compared to the flat jet plate. At a relatively high wave amplitude (A/d ≥ 0.5), the vortex structure underwent significant changes, inducing a higher level of turbulence kinetic energy in the near-wall region of the target chamber. This led to enhanced heat transfer near the stagnation and effusion hole regions compared to the flat double-wall cooling. The effusion hole diameter exerted a minimal effect on the overall Nusselt number of the corrugated double-wall cooling. At very low Reynolds numbers (Rej 〈900), the flow and heat transfer characteristics in corrugated double-wall cooling resembled those observed in flat double-wall cooling.

Effect of nozzles on disease control with spraying fungicides in soybean crops

ABSTRACT The productivity of the soybean crop (Glycine max) can be limited by several factors, including diseases. In the integrated management of diseases, one of the strategies used is chemical control. The aim of this experiment was to evaluate the influence of spray nozzle types on the chemical control of fungal diseases in soybean plants. The experimental design was randomised blocks, with six treatments and four replications. The treatments consisted of control (without fungicide application on soybean plants) and application of fungicides with different spray nozzles: hollow cone jet, double flat jet, extended range flat jet, wide angle flat jet and air induction flat jet. The sprayer used was the backpack pressurised by carbon dioxide CO2. The experiment was installed in the Campos Gerais region (Paraná, Brazil); during three cropping seasons. The evaluated variables were incidence and severity, spray quality (covered area, droplet density, and relative amplitude) and yield components. It was concluded that the chemical control of fungal diseases in soybean plants reduced the proliferation of pathogens and losses in crop yield. There were significant changes in spraying quality in all analysed variables. There were no differences among the spray nozzle types regarding the analysis of incidence, severity and soybean yield components.

Development of a flat jet delivery system for soft X-ray spectroscopy at MAX IV.

One of the most challenging aspects of X-ray research is the delivery of liquid sample flows into the soft X-ray beam. Currently, cylindrical microjets are the most commonly used sample injection systems for soft X-ray liquid spectroscopy. However, they suffer from several drawbacks, such as complicated geometry due to their curved surface. In this study, we propose a novel 3D-printed nozzle design by introducing microscopic flat sheet jets that provide micrometre-thick liquid sheets with high stability, intending to make this technology more widely available to users. Our research is a collaboration between the EuXFEL and MAX IV research facilities. This collaboration aims to develop and refine a 3D-printed flat sheet nozzle design and a versatile jetting platform that is compatible with multiple endstations and measurement techniques. Our flat sheet jet platform improves the stability of the jet and increases its surface area, enabling more precise scanning and differential measurements in X-ray absorption, scattering, and imaging applications. Here, we demonstrate the performance of this new arrangement for a flat sheet jet setup with X-ray photoelectron spectroscopy, photoelectron angular distribution, and soft X-ray absorption spectroscopy experiments performed at the photoemission endstation of the FlexPES beamline at MAX IV Laboratory in Lund, Sweden.

Molecular beam scattering from flat jets of liquid dodecane and water

AbstractMolecular beam experiments in which gas molecules are scattered from liquids provide detailed, microscopic perspectives on the gas–liquid interface. Extending these methods to volatile liquids while maintaining the ability to measure product energy and angular distributions presents a significant challenge. The incorporation of flat liquid jets into molecular beam scattering experiments in our laboratory has allowed us to demonstrate their utility in uncovering dynamics in this complex chemical environment. Here, we summarize recent work on the evaporation and scattering of Ne, CD4, ND3, and D2O from a dodecane flat liquid jet and present first results on the evaporation and scattering of Ar from a cold salty water jet. In the evaporation experiments, Maxwell–Boltzmann flux distributions with a cosθ angular distribution are observed. Scattering experiments reveal both impulsive scattering (IS) and trapping followed by thermal desorption (TD). Super‐specular scattering is observed for all four species scattered from dodecane and is attributed to anisotropic momentum transfer to the liquid surface. In the IS channel, rotational excitation of the polyatomic scatterers is a significant energy sink, and these species accommodate more readily on the dodecane surface compared to Ne. Our preliminary results on cold salty water jets suggest that Ar atoms undergo some vapor‐phase collisions when evaporating from the liquid surface. Initial scattering experiments characterize the mechanisms of Ar interacting with an aqueous jet, allowing for comparison to dodecane systems.Key Points Molecular beam scattering from flat liquid jets is a powerful technique to elucidate mechanistic detail at the gas–liquid interface. Previous dodecane scattering experiments have uncovered angularly‐resolved thermal desorption fractions and energy transfer at the interface for several small molecule scatterers. Preliminary results on scattering from cold salty water reveal mechanisms of interaction between argon and an aqueous jet.

A sub-100 nm thickness flat jet for extreme ultraviolet to soft X-ray absorption spectroscopy.

Experimental characterization of the structural, electronic and dynamic properties of dilute systems in aqueous solvents, such as nanoparticles, molecules and proteins, are nowadays an open challenge. X-ray absorption spectroscopy (XAS) is probably one of the most established approaches to this aim as it is element-specific. However, typical dilute systems of interest are often composed of light elements that require extreme-ultraviolet to soft X-ray photons. In this spectral regime, water and other solvents are rather opaque, thus demanding radical reduction of the solvent volume and removal of the liquid to minimize background absorption. Here, we present an experimental endstation designed to operate a liquid flat jet of sub-micrometre thickness in a vacuum environment compatible with extreme ultraviolet/soft XAS measurements in transmission geometry. The apparatus developed can be easily connected to synchrotron and free-electron-laser user-facility beamlines dedicated to XAS experiments. The conditions for stable generation and control of the liquid flat jet are analyzed and discussed. Preliminary soft XAS measurements on some test solutions are shown.

Https://vestnik.mrsu.ru/index.php/en/articles2-en/123-24-1/1114-10-15507-0236-2910-034-202401-5

Introduction. The article describes the process of considering the geometric parameters of water jet depending on a water jet operation mode and nozzle type. Within the framework of the study of hydraulic soil treatment in the under-tree zones, it became necessary to study the water jet parameters when using different types of nozzles. There was need to determine the geometric parameters of water flow for calculating the cross-sectional area and determining the structural features of the water jet formation. These characteristics are important for a complete description, subsequent study and calculation of water jet action during hydraulic soil treatment; they also allow studying the real shape and structure of the water jet when using different types of nozzles. Aim of the study. The study is aimed at determining the geometric parameters of the water jet for different nozzles including turbo cutters located at different heights. Materials and Methods. To solve this problem, there was developed a test bench, on four pillars, to which the adapter of the supply line of the high-pressure apparatus with replaceable nozzles is fixed. To fix the position and shape of the water jet with a certain frequency, a Basler ace acA1920 camera was used. There was also used a high-pressure apparatus with a maximum pressure of P = 140 MPa, a maximum flow rate of Q = 360 l/h. A standard nozzle with a flat jet, a standard turbo nozzle, and a turbo nozzle of the developed design were used. The geometric parameters of the water jet section were measured from the photographs obtained. Results. From the photos obtained, it can be seen that the rotating water stream entering the turbo nozzle of its own design and the standard turbo nozzle disintegrates from rapid rotation, forming a cone, the cross-sectional area of which is a circle, and affects the soil surface. A flat jet is characterized by a rectangular cross-section. Discussion and Conclusion. According to the results of the study we can draw the following conclusions, the nozzle of the proposed design allows creating water jets of the largest area, which should provide an increase in the working width and, as a consequence, an increase in productivity and quality of soil surface treatment in mainline plantations. This study will also make it possible to analyze the structure of the jet during its operation.

Analysis of Confined Jet Impingement in Converging Annular Microchannel Heat Sinks

Jet impingement cooling is deemed an excellent choice for the thermal management of high-power electronics. However, high-pressure drop penalties and low local heat transfer coefficients in regions far from the jet zone are its drawbacks. Although it is reported that recirculation areas appear because of the entrainment, the effects of recirculation size on thermal behavior are not understood well enough. Here, jet impingement heat sinks with converging annular channels are employed in a numerical investigation to minimize the adverse cooling effects associated with an impinging jet in a microchannel. The realizable k−ε turbulent model is used for modeling thermal and turbulent flow fields (Re=5,000 to 25,000). It was found that the different flow recirculation zones in small scales are responsible for the enhanced heat transfer rate. While the thermal performance of a converging wall jet impingement heat sink is higher than its flat wall counterpart at low Re numbers, the thermal performance results are in favor of the flat wall jet impingement heat sink at high Re numbers. The flow recirculation area shrinks in converging channels at high Re numbers, thereby deteriorating the thermal performance of the converging channel compared with a flat wall jet heat sink. Also, it was found that employing steeper converging channels shrinks the flow recirculation region, resulting in up to 59% lower pressure drops at Re=25,000. The present study examines the role of flow recirculation at different Re numbers on the thermohydraulic performance of jet impingement converging annular heat sinks.

Molecular beam scattering of ammonia from a dodecane flat liquid jet.

The evaporation and scattering of ND3 from a dodecane flat liquid jet are investigated and the results are compared with previous studies on molecular beam scattering from liquid surfaces. Evaporation is well-described by a Maxwell-Boltzmann flux distribution with a cos θ angular distribution at the liquid temperature. Scattering experiments at Ei = 28.8 kJ mol-1 over a range of deflection angles show evidence for impulsive scattering and thermal desorption. At a deflection angle of 90°, the thermal desorption fraction is 0.49, which is higher than that of other molecules previously scattered from dodecane and consistent with work performed on NH3 scattering from a squalane-wetted wheel. ND3 scattering from dodecane results in super-specular scattering, as seen in previous experiments on dodecane. The impulsive scattering channel is fitted to a "soft-sphere" model, yielding an effective surface mass of 55 amu and an internal excitation of 5.08 kJ mol-1. Overall, impulsively scattered ND3 behaves similarly to other small molecules scattered from dodecane.

Dynamics of photoexcited 5-bromouracil and 5-bromo-2'-deoxyuridine studied by extreme ultraviolet time-resolved photoelectron spectroscopy in liquid flat jets.

The UV-induced photo-relaxation dynamics of 5-bromouracil (BrU) and 5-bromo-2'-deoxyuridine (BrUrd) in aqueous solution were investigated using femtosecond time-resolved photoelectron spectroscopy with an extreme ultraviolet (XUV) probe in a flat liquid jet. Upon excitation to the 1ππ* state by 4.66 eV UV photons, both molecules exhibited rapid relaxation into lower-lying electronic states followed by decay to the S0 ground state. By employing a 21.7 eV XUV probe pulse, we were able to differentiate the relaxation of the excited state population from the initially excited 1ππ* state to an intermediate electronic state with 100 fs. Computational results identify this intermediate as the 1πσ* excited state, accessed by a 1ππ*/1πσ* conical intersection, and the signal from this intermediate state disappears within ∼200 fs. In contrast to thymine, formation of neither the 1nπ* state nor a long-lived triplet state was observed. Although the 1πσ* state is largely repulsive, prior studies have reported a low quantum yield for dissociation, and we observe weak signals that are consistent with production of hot S0 ground state (for BrUrd) on a time scale of 1.5-2 ps. It thus appears that solvent caging effects limit the dissociation yield in solution.

Extreme ultraviolet time-resolved photoelectron spectroscopy of adenine, adenosine and adenosine monophosphate in a liquid flat jet.

Time-resolved photoelectron spectroscopy using an extreme-ultraviolet (XUV) probe pulse was used to investigate the UV photoinduced dynamics of adenine (Ade), adenosine (Ado), and adenosine-5-monophosphate (AMP) in a liquid water jet. In contrast to previous studies using UV probe pulses, the XUV pulse at 21.7 eV can photoionize all excited states of a molecule, allowing for full relaxation pathways to be addressed after excitation at 4.66 eV. This work was carried out using a gas-dynamic flat liquid jet, resulting in considerably enhanced signal compared to a cylindrical jet. All three species decay on multiple time scales that are assigned based on their decay associated spectra; the fastest decay of ∼100 fs is assigned to ππ* decay to the ground state, while a smaller component with a lifetime of ∼500 fs is attributed to the nπ* state. An additional slower channel in Ade is assigned to the 7H Ade conformer, as seen previously. This work demonstrates the capability of XUV-TRPES to disentangle non-adiabatic dynamics in an aqueous solution in a state-specific manner and represents the first identification of the nπ* state in the relaxation dynamics of adenine and its derivatives.

Numerical modelling and analysis of porous surface-enhanced jet cooling using copper inverse opals in single-phase flow

Abstract In this study, we propose a novel cooling scheme that utilizes copper inverse opals (CIOs) for surface enhancement in a single-phase impingement jet cooling system. We perform computational fluid dynamics simulations to evaluate the cooling performance of the CIO jet coolers. Our modelling results indicate that the proposed CIO-coated cooler can significantly reduce the average temperature and improve the temperature uniformity across the entire chip surface. The average Nusselt number of the CIO-coated cooler can reach up to 2.8 times that of the flat surface jet cooler. However, the porous structure of the CIO-coated cooler increases the total pressure drop. To determine designs with high cooling performance and low energy consumption, we investigate two crucial design factors, namely the inlet velocity and the nozzle-to-CIO distance. Our analysis reveals that increasing the inlet velocity further enhances the heat transfer, but at the expense of high pressure drop. On the other hand, a larger nozzle-to-CIO distance results in a lower pressure drop but also reduces the heat transfer coefficient. The effects of nozzle-to-CIO distance are further understood by studying the flow resistance network. Furthermore, we present a reduced-order model that accurately captures the thermofluidic characteristics of the proposed design.

Physical and Numerical Simulation Study on Structure Optimization of the Inner Wall of Submerged Entry Nozzle for Continuous Casting of Molten Steel

The submerged entry nozzle (SEN) plays an important role in the continuous casting production process. It is a cast refractory pipe fitting installed in the lower part of the tundish and inserted below the molten steel level of the mold. It not only affects the speed of molten steel flow, but is also prone to nodules and affects production. In the present work, the flow behavior of molten steel in a traditional nozzle and that in a new type of nozzle whose inner wall was distributed with arrays of hemispherical crowns were studied by means of both physical simulation (using a water model) and numerical simulation (using ANSYS CFX) based on the prototype of a production continuous casting slab mold. Both experimental and numerical simulation results show that, compared with the traditional nozzle, the impact depth generated by the new-type nozzle in the mold is reduced by 21.06–26.03 cm, the impact angle is reduced by 14–17 degrees, and swirl flow was generated inside the new-type nozzle, which not only improves the flow characteristics inside the submerged entry nozzle and changes the dead zone size in the submerged entry nozzle, but also improves the velocity distribution at the outlet of the nozzle and minimizes the possibility of nodulation. In addition, in contrast to the traditional nozzle that generates flat body-shaped jets of molten steel flow, the new-type nozzle produces baseball glove-shaped jets that penetrate shallower into the molten steel bath in the mold, which significantly reduces the outlet velocity and is conducive to the floating of inclusions.

Experimental capabilities for liquid jet samples at sub-MHz rates at the FXE Instrument at European XFEL.

The Femtosecond X-ray Experiments (FXE) instrument at the European X-ray Free-Electron Laser (EuXFEL) provides an optimized platform for investigations of ultrafast physical, chemical and biological processes. It operates in the energy range 4.7-20 keV accommodating flexible and versatile environments for a wide range of samples using diverse ultrafast X-ray spectroscopic, scattering and diffraction techniques. FXE is particularly suitable for experiments taking advantage of the sub-MHz repetition rates provided by the EuXFEL. In this paper a dedicated setup for studies on ultrafast biological and chemical dynamics in solution phase at sub-MHz rates at FXE is presented. Particular emphasis on the different liquid jet sample delivery options and their performance is given. Our portfolio of high-speed jets compatible with sub-MHz experiments includes cylindrical jets, gas dynamic virtual nozzles and flat jets. The capability to perform multi-color X-ray emission spectroscopy (XES) experiments is illustrated by a set of measurements using the dispersive X-ray spectrometer in von Hamos geometry. Static XES data collected using a multi-crystal scanning Johann-type spectrometer are also presented. A few examples of experimental results on ultrafast time-resolved X-ray emission spectroscopy and wide-angle X-ray scattering at sub-MHz pulse repetition rates are given.

Performance analysis of a novel flat lay-type synthetic jet pump with Y-shaped jet chamber.

Recently, synthetic jet pumps have been expected to be used in electronic heat dissipation devices due to the vortex suction phenomenon for transporting fluids. Aiming to improve the delivery ability of the jet pump to output fluid continuously, a novel flat lay-type synthetic jet pump (FLTSJP) with a Y-shaped jet chamber is proposed in this paper. Based on the synthetic jet effect, the pump chamber continuously outputs fluid in one cycle. The output performance of FLTSJP is theoretically analyzed to be affected by the outlet cone angle. The one-cycle flow mechanism of the fluid in the Y-shaped jet chamber is simulated. FLTSJP is manufactured, and a test system is built. Experiments show that the Y-shaped jet chamber effectively improves the output performance. The optimum flow rate and outlet pressure were both reached at 160V and 40Hz, which were 20.63 ml/min and 333.43Pa, respectively. This FLTSJP effectively improves the output performance of synthetic jet pumps and provides a new research concept of water-cooled devices for electronic heat dissipation.

Flat jet electrochemical milling of TC4 alloy with tailoring backward parallel flow

In flat jet electrochemical milling, the electrolyte forms a backward parallel flow after impacting the workpiece, resulting in a weak current density distribution on the workpiece. Poor surface quality usually occurs on the machined titanium alloy surface because it inevitably suffers from the weak current density. In this study, a method of flat jet electrochemical milling with tailoring the backward parallel flow was proposed to eliminate the negative effects caused by the weak current density. Multiphysics simulations are carried out to comprehend the mechanism of flat jet-EC milling with tailoring backward parallel flow and better construct the novel tool electrode. Experiments on flat jet electrochemical milling of TC4 alloy with and without tailoring backward parallel flow are conducted. The results reveal that, compared with flat jet electrochemical milling without tailoring backward parallel flow, the recommended tool reduces the surface roughness by 86% to 93%, and improves the material removal rate by 93% to 163% with different feed rates. Additionally, the recommended tool is more conducive to maintaining the inherent hardness of the material. Finally, a surface with low Sa of 0.37 μm is obtained.

Evaporation and scattering of neon, methane, and water from a dodecane flat liquid jet.

The evaporation and scattering of Ne, CD4, and D2O from a dodecane flat liquid jet are investigated in a molecular beam apparatus. The experiment yields translational energy distributions as a function of scattering angle by means of a rotatable mass spectrometer. In the evaporation experiments, one observes a Maxwell-Boltzmann distribution with a cos θ angular distribution superimposed on a weak, isotropic background. The scattering experiments show contributions from impulsive scattering and thermal desorption. At select incident angles for the three systems, angular distributions show super-specular scattering for the impulsive scattering channel, an effect attributed to anisotropic momentum transfer to the liquid surface. The impulsive scattering channel is analyzed with a soft-sphere model to explore energy transfer between the scatterer and liquid as a function of deflection angle. Compared to Ne scattering, the polyatomic gases exhibit more thermal desorption and, in the impulsive scattering channel, a higher degree of internal excitation.

Spray nozzles for application of fungicides in common bean

common beans (Phaseolus vulgaris) are one of the staple foods for Brazilians. Production can be reduced by the action of unwanted factors, including the occurrence of diseases. In the integrated management of diseases there is the strategy of chemical control. The objective of the study was to evaluate the influence of spray nozzles on the chemical control of diseases in common bean. The experimental design used was in randomized blocks with six treatments and four replications. The treatments consisted of control (without fungicide application on bean plants) and application of fungicides with spray nozzles hollow cone jet, double flat jet, extended range flat jet, wide angle flat jet and air induction flat jet. The sprayer used was the backpack pressurized by CO2. The experiment was conducted in the region of Campos Gerais (Paraná, Brazil) during the 2016, 2017 and 2018 crop seasons. The variables analyzed were the incidence and severity of diseases, spray quality (covered area, density, and relative amplitude) and common bean yield components. It is concluded that the chemical control of fungal diseases in bean plants reduced the action of diseases and losses in productivity. There were significant changes in spraying quality in all variables analyzed. There were no differences among the nozzles regarding the analysis of incidence, severity and yield components of the bean crop.

Electric Traction Motor Spray Cooling—Empirical Model Development and Experimental Validation

The growing interest in electric vehicles leads to new developments of efficient electric traction motors with high power density. Since a large part of the losses in an electric motor can occur in the windings, it is important to cool the windings to reduce the temperature and protect the winding insulation from thermal aging. Oil spray cooling systems are becoming more and more relevant for cooling the windings. In this work, an approach for heat transfer modeling of electric traction motors (power classes #2-4 with 60 to 180kW) with hairpin end windings is developed and tested. The model is developed with a testing rig for different flat jet spray nozzle arrangements for a hairpin electric traction motor. The model approach showed a good agreement with the measured temperatures of the end windings in the testing rig. A transient thermal simulation of the testing rig confirms the good agreement. In a second step the model approach is transferred to another electric traction motor with a different spray cooling system. The simulation results of the second electric traction motor also show good agreement with thermal quasi-static operating points and transient measurements at low and medium speed. At high speeds the deviations increased. Possible causes for this behavior are discussed.